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On general relation between quantum ergodicity and fidelity of quantum
dynamics
Tomaz Prosen
abstract: General relation is derived which expresses the fidelity of quantum dynamics,
measuring the stability of time evolution to small static variation in the
hamiltonian, in terms of ergodicity of an observable generating the
perturbation as defined by its time correlation function. Fidelity for ergodic
dynamics is predicted to decay exponentially on time-scale proportional to
delta^(-2) where delta is the strength of perturbation, whereas faster,
typically gaussian decay on shorter time scale proportional to delta^(-1) is
predicted for integrable, or generally non-ergodic dynamics. This surprising
result is demonstrated in quantum Ising spin-1/2 chain periodically kicked with
a tilted magnetic field where we find finite parameter-space regions of
non-ergodic and non-integrable motion in thermodynamic limit.
- oai_identifier:
- oai:arXiv.org:quant-ph/0106149
- categories:
- quant-ph nlin.CD
- comments:
- Slightly revised version, 4.5 RevTeX pages, 2 figures
- doi:
- 10.1103/PhysRevE.65.036208
- arxiv_id:
- quant-ph/0106149
- created:
- 2001-06-26
- updated:
- 2001-10-04
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